Currently Star Wars: The Old Republic is in closed beta testing. While a small group of players have received open-ended invites to participate in the beta Bioware has also recently begun a series of "Beta Weekends" to expand the testing population. During each of these weekends a new, random group of players is invited to participate in the testing of The Old Republic. All players are eligible to "opt in" for the opportunity to via Bioware's website.
Players who are selected for these invites will receive instructions for accepting the beta invitation via e-mail sent to the address associated with their SWTOR account. Players can also check on their beta invite status any time by visiting Bioware's website.
During the Paris Games Week it was also stated that the Guild Testing for TOR would be expanded to European players soon.
During the October 27th EA Q2 earnings call COO Peter Moore announced the expansion of the beta weekend program stating; "In the coming weeks, we'll invite hundreds of thousands of players into our biggest beta test to date." 
Previous Beta Events
Beta Weekend #1 took place over Labor Day (US) weekend and was a resounding success with 'every goal meeting or exceeding' Bioware's expectations. 
Beta Weekend #2 took place October 7th through 11th.
Beta Weekend #3 took place October 13th through 18th, this was a smaller test however it also added New Zealander and Australian testers to the pool. 
Beta Weekend #4 took place November 11th 5:00 PM central time to November 13th 11:59 pm central time.
European players are now also eligible for selection in the Beta Weekends. 
The beta testing NDA has been lifted as of 11/18/2011. 
- PGW 2011: Chris Collins Interview http://darthhater.com/2011/10/23/pgw2011-interview-chris-collins/
- EA Q2 Earnings Call Transcript http://seekingalpha.com/article/303029-electronic-arts-ceo-discusses-q2-2012-results-earnings-call-transcript?source=yahoo
- Beta Testing Weekend #1 Update http://www.swtor.com/community/showthread.php?t=479405
- Beta Testing Weekend #3 Update http://www.swtor.com/community/showthread.php?p=9848266#edit9848266
- Chris Collins, European Community Manager http://www.swtor.com/community/showthread.php?t=513133
- The Old Republic Opens Up! http://www.swtor.com/community/showthread.php?p=10939389#edit10939389